In regular open circuits with either a capacitor or inductor element, (when capacitor is uncharged) with a battery, when a switch is closed to complete the circuit the current is said to be 0 because current doesn't jump immediately.

But in a circuit with just resistors, as soon as a switch is closed the current isn't 0?

It's not clear enough what you're having trouble with. Conceptually, yes, current jumps instantly in a battery-resistor circuit. If it is as simple as this, I don't see what you're asking.
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Alan RomingerAug 27 '12 at 19:29

@jak, it's as simple as Ohm's Law. When the switch is instantaneously closed, the voltage across the resistor instantaneously changes from zero to some non-zero value. Thus, by Ohm's Law, the current instantaneously changes from zero to some non-zero value.
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Alfred CentauriAug 28 '12 at 1:56

3 Answers
3

In real life, the current can't jump instantaneously because there is always some finite inductance in a circuit. However, this is just a typical idealized textbook problem where the inductance is assumed identically zero, so the current can jump instantaneously according to the assumptions of the problem. Note the current also jumps in their solution for the capacative case.

This question is working within the realm of 'circuit theory', which is an idealization useful for introductory teaching of electromagnetism. It is really a simplification of electrodynamic field theory, just a special case making useful assumptions. A lot of conceptual problems in circuit based questions come from forgetting that you are dealing with a slightly unreal situation.

The answer is as above, the current does not instantaneously propogate throughout the circuit but at some finite speed $<c$. In introductory problems however this speed is much faster than you need to worry about.

This is really a footnote to user1631's answer: even in the absence of any inductance the current obviously can't change instantly because no signal can propagate faster than the speed of light. In typical circuits the increase in current propagates somewhere between $0.1c$ and $c$.